That is St Augustine. With a little purple at the base it is very likely to be the Floratam variety developed at Florida State and Texas A&M.

I don't see any of the shoots that are characteristic of St. Augustine though?

Okay lets take a closer look. Can you let the new grass grow out to 4 inches and take a picture of it on an overcast day or in the shade of a tree or something? I'm interested in what the tips of the new grass look like. St Augustine has blunt tips.

Does it ever get seed stalks or flowers?

What happens at the edge of the pavement? Does it try to escape?

Here's my take on your first picture.

Thank you! The pointy tips part was key, so I can now ID crabgrass! but what about Carpetgrass? I just mowed but did find a stray seed stalk, that with a little googling appears to be Carpetgrass, which does not appear to have a pointy tip. So now I think my yard is mostly Carpetgrass. I was told by the original owner that St Augustine was planted 20+ years ago but I'm thinking none of it has survived the years.

The red I think is crab grass and the green might be Carpetgrass?

WTH? I'm confused. I don't see any crab grass in your pictures. Also I don't see any St Augustine in the last picture. Here is a picture of crabgrass which has taken over a bermuda lawn.

Carpetgrass: for the most part, carpetgrass is a nickname for St Augustine and/or centipede. Some paspallum plants are called carpetgrass, but it is so rare that almost nobody really has it. You might, though. The key is to let it go unmowed for a full week and see if it develops seed heads. There is another rare grass, Axonopus, which is called carpetgrass. It does grow fairly wild, so if your lawn was ignored for years, you might have the invader.